Hechth–Nielsen theorem for a modified neural network with diagonal synaptic connections
The work suggests a modified three-layer neural network with architecture that has only the diagonal synaptic connections between neurons; as a result we obtain the transformed Hecht-Nielsen theorem. This architecture of a three-layer neural network ($m=2n+1$ is the number of neurons in the hidden layer of the neural network; $n$ is the number of input signals) allows us to approximate the function of $n$ variables, with the given accuracy $\varepsilon>0$, using one aggregation operation, whereas a three-layer neural network that has both diagonal and non-diagonal synaptic connections b